Question

Expand sin (xy) in the powers of (x-1) and (y-π/2) up to the terms of third degree

Answer 1

Step-by-step explanation:(x,π/2−y)

If you know the expansion of ex , then it's quite easy to expand excosy

ex=1+x+x22!+x33!+...

Now, just put xcosy in place of x in the above expression to get:

excosy=1+xcosy+(xcosy)22!+(xcosy)33!+...

Now use the fact that cosy=sin(π/2−y) so that

excosy=1+xsin(π/2−y)+(xsin(π/2−y))22!+(xsin(π/2−y))33!+...=f(x,π/2−y)